Simulating waves in flows by Runge-Kutta and compact difference schemes

Yu, Sheng‐Tao; Hsieh, K. C.; Tsai, Ying-Liang

doi:10.2514/3.12470

Cited by 23 publications

(9 citation statements)

References 11 publications

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“…(30) indicates that the exact solution of (23) may be decomposed in both an spatial and a temporal part. With a Runge-Kutta method, we approximate the temporal part of (23) with a Taylor expansion.…”

Section: Analysis Of the Complete Discretizationmentioning

confidence: 98%

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On the simulation of wave propagation with a higher-order finite volume scheme based on Reproducing Kernel Methods

Nogueira

Colominas

Cueto‐Felgueroso

et al. 2010

Computer Methods in Applied Mechanics and Engineering

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Section: Analysis Of the Complete Discretizationmentioning

confidence: 98%

“…Following [30], the numerical dissipation is given by the magnitude of the amplification factor. When jrðzÞj 6 1 the method is stable.…”

Section: Analysis Of the Complete Discretizationmentioning

confidence: 99%

On the simulation of wave propagation with a higher-order finite volume scheme based on Reproducing Kernel Methods

Nogueira

Colominas

Cueto‐Felgueroso

et al. 2010

Computer Methods in Applied Mechanics and Engineering

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“…The amplification factor of Equation ( 13) discretized by the Runge-Kutta method can be obtained as follows [13]:…”

Section: Stability Analysismentioning

confidence: 99%

Compact Difference Schemes Combined with Runge-Kutta Methods for Solving Unsteady Convection-Diffusion Problems

Zhu

Chen

2021

UJPR

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“…On the other hand, multi-stage single step schemes are parasite free, and therefore present interesting possibilities. High-order Runge-Kutta multi-stage approximations have been used with success (Lele 1992, Zing 1995; Yu et al (1995) examined various combinations of Runge-Kutta time-marching schemes and compact spatial differencing. As a rule, the higher-order varieties of both time and space discretizations provided the best overall performance from the point of view of dispersion and dissipation characteristics, although the authors recommend using a fourth-order rather than a sixth-order compact spatial operator since the lower-accuracy method provided nearly equivalent results at lower computational cost.…”

Section: Time Discretizationmentioning

confidence: 99%

Computing Aerodynamically Generated Noise

Wells

Renaut

1997

Annu. Rev. Fluid Mech.

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In contrast to computational aerodynamics, which has advanced to a fairly mature state, computational aeroacoustics (CAA) has only recently emerged as a separate area of study. Following a discussion of the classical field of aeroacoustics as introduced by Lighthill, the paper provides an overview and analysis of the problems associated with utilizing standard computational aerodynamics procedures for acoustic computations. Numerical aspects of computing sound-wave propagation are considered, including assessments of several schemes for spatial and temporal differencing. Issues of particular concern in computing aerodynamically generated noise, such as implementing surface and radiation boundary conditions and algorithms for predicting nonlinear steepening and shocks, are discussed. In addition, the paper briefly reviews alternatives to the conventional finite-difference schemes, such as boundary-element and spectral methods and the uncommon lattice-gas method. MODERN AEROACOUSTICS Sir James Lighthill (1993b) has stated that the aeronautical community has recently entered into the second Golden Age of Aeroacoustics. The first of these eras, as defined by Lighthill, focused on the problems of jet noise and jet engine noise, and lasted from the late 1940s until the mid 1970s. By that time, high-bypass-ratio turbine engines had become the standard for all new transport aircraft, and the initially excessive noise produced by turbojets had been

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Simulating waves in flows by Runge-Kutta and compact difference schemes

Cited by 23 publications

References 11 publications

On the simulation of wave propagation with a higher-order finite volume scheme based on Reproducing Kernel Methods

On the simulation of wave propagation with a higher-order finite volume scheme based on Reproducing Kernel Methods

Compact Difference Schemes Combined with Runge-Kutta Methods for Solving Unsteady Convection-Diffusion Problems

Computing Aerodynamically Generated Noise

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